Marten Scheffer gave a keynote at the Complexity conference last Fall about critical slowing down  phenomenon indicating tipping points.   Flickering  is a different signature.   We had a good conversation about our ECS and Synthesis.   ( He’s also quite into the sound scene and dabbled in sonification early in his career. )   We should contact him as well as Alex Penn for our ECS workshop, maybe Skype? 

Maybe here’s how we can think of both phenomena: Consider a model  R¹  x M where   R¹  is the single time dimension and M are the non-temporal dimensions of the model.    Let  f: R¹ x M —> R¹ be any (differentiable) scalar function.

Look at the partial derivatives of f.   Maybe if the second time-derivative  is close to 0 we get the phenomenon of critical slowing down.   But if the second time derivative is positive we get flickering.   Correlation lengths depend on the partial derivatives w/r to M

Is this correct?

Xin Wei

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2. Dearing, J. A. et al. Extending the timescale and range of ecosystem services through paleoenvironmental analyses: the example of the lower Yangtze basin. Proc. Natl Acad. Sci. USA 109, E1111–E1120 (2012)